Integration from 0 to infinity x2 / (xsinx ecosx)2

2 years ago


Answers : (1)

                                        integral lim x=0 to infinity x^2/x^2sin^2xe^2cos^2x
=integral lim x=0 to infinity 1/sin^2xe^2cos^2x
=1/e^2integral lim x=0 to infinity4/(2sinxcosx)^2
=4/e^2integral lim x=0 to infinity dx/sin^2(2x)
=4/e^2 integral lim x=0 to infinity cosec^2(2x) dx
=4/e^2 [(-cot2x)/2] x=0 to infinity
=2/e^2[-cot infinity+ cot0]
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Rinkoo Gupta
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